In this type of pump, a pump is generally mounted on a reservoir containing the fluid, and is actuated by means of a dispensing head or pusher, assembled onto said pump. The pump generally comprises a pump body in which a piston is mounted to slide between a rest position and an actuating position. The piston is generally connected to an actuating rod adapted to transmit the manual actuation force exerted by the user on the head or pusher. An abutment element, such as a ferrule, is generally assembled in the top edge of the pump body, to define the rest position for said piston. The ferrule generally extends inside the pump body, so that the actuating rod slides inside said ferrule. Sealing between the actuating rod and the pump is generally provided at the piston which is mounted to slide in leaktight manner inside said pump body. The sealing between the pump body, the ferrule, and the fixing ring is generally provided by means of a gasket that is interposed between said pump body and said fixing ring. The coupling between the actuating rod and the ferrule is not necessarily leaktight because sealing is provided by the above-described sealing points. Pumps of the above-described type operate satisfactorily but they suffer from some drawbacks. Thus, when the user exerts an actuating force that is not exactly axial, the actuating rod can be moved off center while it is being actuated, which can give rise to the pump malfunctioning or becoming difficult to actuate. Similarly, since the actuating rod does not necessarily co-operate in leaktight manner with the ferrule, there can be some play between those two elements, so that the actuating rod is not necessarily centered relative to the ferrule and therefore relative to the pump body, which can give rise to the pump malfunctioning while it is being actuated.